BANGKOK — The head of Thailand’s military government, Prayuth Chan-ocha, said on Tuesday that security forces had arrested a man they believe planted the bomb that killed 20 people in Bangkok two weeks ago.

Just hours after the arrest along the border between Thailand and Cambodia, a police spokesman, Lt. Gen. Prawut Thavornsiri, said the authorities were confident that the man was “a key perpetrator in this case.”

But in an investigation that has been criticized for a number of false leads, the police acknowledged that they had minimal evidence to substantiate their suspicions.

“We don’t have the evidence yet,” said General Prawut, adding that the man was charged with trying to cross the border illegally. He said the authorities had yet to conduct a DNA test and other forensic exams.

It was the second arrest since the Aug. 17 attack, the worst bombing in recent Thai history, which struck in the heart of Bangkok’s main shopping district.

The police said they did not know the nationality of the man who was detained on Tuesday, but they said he was foreign.

The authorities have been searching for a man who was seen in a video placing a backpack under a bench near the Erawan Shrine minutes before the explosion. Mr. Prayuth said the suspect who was arrested on Tuesday “looks similar” to the man in the security camera footage, but he added that the police would proceed with other procedures, including a fingerprint analysis.

Thai news media showed an image of a lanky man with the beginnings of a beard in the custody of soldiers. The Thai police said that he was arrested as he was trying to cross the border into Cambodia and that he spoke to the authorities in English.

Mr. Prayuth said the man had sought to evade security forces before being detained.

“He was trying to escape,” he said.

“We are looking for the bomber, the person who ordered it and the person who used a phone,” he said, without elaborating. “We have to arrest them all.”

The first arrest in the investigation was announced on Saturday. That man was also said to be a foreigner; his name and nationality have also not been released.

On Monday, the authorities issued two arrest warrants in connection with the case, one of them for Wanna Suansan, a woman from a Muslim area in southern Thailand whose family said she had moved to Turkey weeks before the bombing. Her village headman, acting as a spokesman, said she was innocent and willing to come back to Thailand to prove it.

He said on Tuesday that family members were shocked when they saw news of the warrant because the police had not contacted them beforehand.

The authorities issued three additional arrest warrants on Tuesday, including for two men they identified as Ahmet Bozoglan and Ali Jolan. The warrant for Mr. Bozoglan included what appeared to be a Turkish identity document. They released a sketch of the third man, whom they described as Turkish but whose identity they did not know.

The Thai government, which has been run by the military since a coup last May, has been vague about possible motives behind the shrine attack. But General Prawut, the police spokesman, on Tuesday offered some of the most detailed comments yet on the group that is believed to have carried it out.

He called the perpetrators members of a “syndicate” involved in smuggling people across borders and producing fake passports. The police discovered 200 such documents in the Saturday raid that produced the first arrest.

General Prawut said the syndicate might have been angered by a crackdown on human trafficking in recent months. “This may have been a revenge attack,” he said on a Thai television program on Tuesday. “They held a grudge against officials.”

After the discovery of mass graves this year along the country’s border with Malaysia, Thai officials bowed to foreign pressure and vowed to dismantle a thriving industry built around smuggling refugees and migrants, mainly from Myanmar and Bangladesh, to Malaysia, where such migrants have traditionally sought work.

But the network described by General Prawut appears to be distinct from those illicit operations, which focused on Southeast Asia. The suspect arrested on Saturday had a crude counterfeit of a Turkish passport, and the 200 fake documents seized during his arrest were also meant to pass as Turkish.

General Prawut said that the Thai authorities had passed on information about the suspect arrested on Saturday to the Turkish authorities and that the Turks were trying to help identify his nationality.

Security analysts have speculated that the attack may have been carried out by members of the Uighur ethnic minority, a Turkic-speaking group living in northwestern China. The attack, they say, may have been revenge for Thailand’s repatriation of more than 100 Uighurs to China in July.